Important

In the future all pages covering analog computing,
its techniques, technology, application etc. will slowly be moved to
a new location at
http://www.analogmuseum.org.
This is the result of the growing size of the collection and
documentation and the wish to have a central point in the web to
gather information about analog computing.

The following pages are becoming obsolete and will not be
developed further!

My enthusiasm for analog computers (especially electronic analog
computers) started when I was young and read the book "Kybernetische
Maschinen" written by Helmar Frank. In this book was a picture of a
huge analog computer, a TELEFUNKEN RA 800. I was instantly hooked by
the idea of dircetly performing calculations by setting up electronic
circuits. The inherent speed and immediacy and mathematical beauty of
this kind of computing fascinates me since then.

Apart from my digital machines (cf. my
computer room)
I started to experiment with simple operational amplifier circuits back
in school. When I got my first TELEFUNKEN
RAT700
analog computer, this was the beginning of my collection
of (mostly) electronic analog computers.

The following pages will eventually contain an introduction into
the art of analog computing as well as detailed descriptions of the
machines in my collection. As one can see, I am still working on these
pages since it is quite time consuming to describe the machines and
to write an introductory course. So currently there are only a couple
of links to my machines and to some other interesting material
concerning analog computing.

Some of my machines:

This machine, the Telefunken
RA 770, is,
in my humble oppinion,
the best and most fascinating electronic analog computer ever
built by any company. With this machine a dream dating back to the
days of my childhood finally came true.

The TELEFUNKEN
RA742
analog computer - this was the last of TELEFUNKEN's very successful
table top analog computers.

The TELEFUNKEN
OMS 811
dual beam oscilliscope. This oscilloscope was especially designed to
be used in conjunction with TELEFUNKEN's transistorized analog
computers. It features two channels with independent x- and
y-deflection as well as synchronisation mechanisms for camera
control, etc.
Here
you can find some notes about the restoration of such an
oscilloscope.

The TELEFUNKEN
DEX102
"Digitalzusatz". This was a digital extension for the
RA742
table top analog computer. Both devices together build a small
hybrid computer.

The Hitachi-240
analog computer. This system has 40 chopper stabilized operational
amplifiers and a lot of special functions, but is quite a challenge
to repair and maintain.

The EAI TR-10
analog computer. This is the first transistorized table top analog
computer built by EAI (1961).

The EAI-2000
analog computer. This is one of the last analog computers built by
this famous company. It is a rather small hybrid computer system
featuring a built in digital prozessor with a control terminal which
allows complete control of the digital part as well as the analog
part of the machine.

The Dornier
DO-960 analog computer. This system is one of the most
sophisticated analog computers ever built.

The Dornier
DO-80 analog computer. The smallest system built by the
German manufacturer Dornier.

The Solartron
Analogue Tutor. A small tube based system intended primarily for
educational purposes.

The
MEDA 43 analog/hybrid
computer. This machine was designed and built in the former
czechoslovakia and found widespread use in the countries behind the
iron curtain.

Some homebrew devices

A four channel X/Y oscilloscope multiplexer. This devices allows
the simultaneous display of up to four figures on an oscilloscope
screen which is quite useful for simulations incorporating a
user interface or simulations which require the observation of
up to four curves during a run.

Many simulations involving a man in the loop require some kind of
a control stick. The device shown on the left is a control stick
adapter to be used in conjunction with an analog computer.

A lot of simulations and stochastic computations require a very
good low frequency random noise source. Using a commercial random
noise generator like the Wandel und Goltermann RG-1, this
special filter delivers a very narrow band low frequency signal
suitable for analog computation.

What is analog computing about?

The following links point to introductory material covering the
technology of analog computers, the art of programming these machines
and their history.

The slides for a talk with the title "Faszination Analogrechnen" which
I gave at the University of Hamburg on February 6th, 2008, may be
found here
(in German, about 1.6 MB).

Since I will talk about analog and hybrid computing at the
VCFE 7.0 (2006) in Munich, I
prepared some slides for this talk which may be found here:
Analog and Hybrid Computing
- an introduction to analog and hybrid computing.

Workshop - Analog Computing
- slides covering the solution of three typical problems on an
analog computer in detail. These examples are 1) mass-spring-damper
system, 2) Lynx/Rabbit ecosystem and a 3)
bouncing ball in a box. These slides (about 700 kB) were prepared
for a talk
to be given at the VCFE 7.0
2006 in Munich.

The following slides,
Telefunken Analog and Hybrid Computers
, give a short overview of Telefunken's developments in the area
of analog and hybrid computing (about 4.5 MB). I created these slides
for a talk to be given at the
VCFE 7.0 2006 in Munich.

My personal favourite link is the one to EAI's multimedia lecture
Understanding the ANALOG/HYBRID Computer. This course gives a
simple introduction to the principles of an analog computer with some
examples. The original lecture consisted of eighty slides and a
corresponding audio tape. Both have been merged into a podcast by
my friend Christian Peters.

Another interesting resource are the
annotations for an ancient slide collection covering the
TELEFUNKEN analog computers -
Dia-Reihe Analogrechner, in German, 27 MB!

A
Practical Approach to Analog Computers by John D. Strong and
George Hannauer gives a good introduction to analog
computing using the then new EAI-231R tube based analog computer,
one of the finest instruments ever made.

Joe Sousa maintains the
Philbrick Archive - an incredibly valuable collection of materials
about Philbrick's operational amplifiers etc. If you are looking for
more information about the famous K2-W amplifier or the like this is
the right place.

Live analog computing:

Have you ever wondered who a rendezvous in space is performed when two
space craft shall be coupled together like the CM/LEM or a Space
Shuttle and the ISS etc.? If so, you might want to have a look at
a simple orbital rendezvous
simulation I programmed this weekend (12/13-JAN-2008).

A couple of days ago I reimplemented the vehicle simulation listed
below on my EAI 580 analog computer using no special external equipment
like the
four
channel oscilloscope multiplexer, etc. This was possible since the
EAI 580 features quite a few electronic analog switches which can
be employed to implement a display multiplexer on the computer itself.
This new simulation is more realistic than the old one below and shows
the car frame, the wheels and the road itself in motion. Read more
about this simulation here.

On September 22nd, my friend Dr. Karina Schreiber (a mathematician, too)
came for a visit and we had lots of fun creating some artwork using
an analog computer. Some of the pictures we created can be seen
here.

On December 1st, 2007, I finished a more complex program on the
Telefunken
RA 770
analog computer to display a so called Joukowski airofoil with lines of
airflow around this profile. The first
video clip (about 8 MB!) shows a single line of airflow around
this airofoil under manual control while the
second video clip (about 2
MB) shows the automatic generation of a family of 16 curves using
the very same program which is described in more detail
here.

Last weekend I developed a small analog computer program to display
rotating three dimensional figures on an oscilloscope screen -
this program together with a short movie of a rotating spiral
can be found here.

Simulating a (simplified)
car suspension
system - this page contains links to three AVI-files showing the
overall setup of a complex simulation run on an analog computer as well
as showing the real time simulation output.

Programming a bouncing
ball in a box - this link leads to a page showing the overall
program, setup and an AVI-file showing the bouncing ball. There also
is a set of slides
describing the simulation in detail.

Watch two
rotating circles
spinning. This film was taken from the display of the
OMS 811
dual beam oscilloscope connected to the
RA742
analog computer.

This short
film
shows an ink plotter in action which plots a quite beautiful
curve generated by the
RA742
analog computer.

The following
film shows
a single rotating circle generated by the
EAI-2000
analog computer.

Persons:

On 29-MAY-2006 my wife and I had the pleasure to have Prof. Giloi
with his wife and Prof. Lauber with his wife as our guests. Some
photos of this event which was very significant for me can be
found here.

Mr. Bruce Baker, a former employee of Martin-Marietta and analog
computing kindly scanned some pictures and papers related with his
work on aerospace simulation
using analog computers.

On 29-APR-2007 my wife and I were
invited by Prof. Dr. Meyer-Brötz, the father of the first
transistorized analog computers made by Telefunken. His first two
machines were the RA 800 and the
RAT 700,
developed in 1959/1960. Prof. Dr. Meyer-Brötz left the area of
analog computing in 1966 when he realized that digital computers
would eventually supersede analog computers in terms of computing
power. His interests shifted to electronic character recognition and
the
like in the following years. It was a wonderful experience and a gift
to meet him and his wife in person. He has lots of memories of the time
of his analog computer developments at Telefunken and is a truly wise
man. This
picture
was taken by his wife at the end of our visit. He sent it to us with
this short handwritten
note.

Thanks to my friend Christian Peters who worked hard for many
hours this EAI lecture is now available as podcast including
audio and synchronized video (slides :-) )
here (about 17 MB). If you are interested in the audio data
only, you can find a 16 MB mp3 coded file
here.

Thanks to my friend Hans
Kulk who sent me a copy of the following, you can now
download the complete
TELEFUNKEN ZEITUNG, Jahrgang 29, 1966, Heft 1,
Herausgeber Prof. Dr. W. T. Runge (German, about 17 MB!).
This wonderful publication describes the development of a high
precision operational amplifier as used in TELEFUNKEN's
analog computers, it covers the RA 800 Hybrid, describes in detail
the technology of function generation, etc. A truly remarkable
publication and a must read for anyone interested in analog
computing.

Thanks to Mr. Böhringer from the Universität Karlsruhe
you can find here
a so called "Studienarbeit" describing the development of a
control system to implement a magnetic suspension (a hovering
metal ball :-) ) - about 20 MB.

Other resources in the internet:

Applied Dynamics International, ADI
for short, made wonderful analog computers from 1957. Although they
have stopped their analog computing business their web site still has
two real treasures about analog computing:

Doug Coward's online
Analog Computer
Museum. He has wonderful and quite complete pictures of the
various models from different manufacturers. Further more there
is a great
introduction
into the art of analog computing.

My friend
Hans
Kulk, a composer, is not only enthusiastic about analog computers
as I am, he also uses his machines to create and compose music.

Building your own analog computer:

Maybe you think, as I constantly do, about building your own analog
computer. If so, here are some topics which should be considered before
attempting such an endeavor:

If you want to build just a small scale demonstration model you can
easily choose off the shelf operational amplifiers, 1% resistors and
some selected off the shelf capacitors to build your computer. Using
relays for controlling the integrators is perfectly fine for such a
computer since you most probably just want to have a way to select
between the three basic modes of operation: Initial condition (called
"Pause" in German), compute ("Rechnen") and Hold ("Halt").

If you think about building something more sophisticated as I do, you
should at least take the following points into account:

Operational amplifiers:

Gain:
This is by far the most complicated and important point when you
intend to build an analog computer suitable for doing real work.
Since the assumption of an inifite gain does not hold for real
world operational amplifiers computing elements based on these
devices will have some inherent errors due to the finite gain.
These errors correlate with the gain and grow smaller as the gain
gets larger. Professional operational amplifiers used in precision
analog computers like the Telefunken
RA741 and
other machines have DC gains of about 1000000000 (10 to the power
of nine)! Gains like this are not easily obtained using modern
integrated circuit operational amplifiers.

Drift and noise:
Every real world operational amplifier is subject to errors due
to drift effects (which correlate with temperature and other
factors) and noise. Noise is indeed a problem but not as much as
drift is since noise tends to cancel out in calculations in the
long run. Drift is a more severe problem since even tiniest drift
effects will accumulate in the integrators of a computer setup.
The most effective and widely used scheme to keep drift effects
negligibly small is to use two amplifiers: One AC coupled main
amplifier, since AC coupled amplifiers do not expose drift effects,
and a chopper stabilized auto zero amplifier. The raw idea is
described in the description of my Telefunken
RA741.
Noteworthy at this point is that the chopper stabilized amplifier
(I would suggest using something like MAXIM's
MAX430
for the auto zero amplifier) will sample the voltage at the summing
point of the main amplifier which should be zero all the time
(synthetic ground). Drift effects in the main amplifier will result
in a non-null voltage at the summing point which will be amplified
by the auto zero amplifier and fed back into the main amplifier's
non-inverting input thus canceling out the drift effect. So building a
suitable operational amplifier for a precision analog computer will
at least require the use of two operational amplifiers - I would
suggest using an OPA27 or the like for the main amplifier and
the already mentioned MAX430 as the auto zero amplifier.

Overload indication:
Every analog computer requires some means of overload indication
which can be used to stop a calculation as soon as an operational
amplifier either

exceeds the value of +/- 1.1 machine units at its output or

is overloaded in a way that requires a higher output
current than the amplifier can readily deliver.

The first topic can easily accomplished by using two comparators
which will generate an output signal as soon as the output voltage
of the main amplifier goes out of bound. The second topic is not
as easily accomplished as this. Measuring the voltage drop over
a series resistor in the output lead of the main amplifier is
generally a bad idea since this resistor will introduce additional
errors in the calculations. The best method to detect this kind of
overloading is to measure the voltage at the summing junction of
the main amplifier. This voltage will be zero at all times under
normal (non-overload) conditions since the auto zero amplifier will
always generate a proper correctional signal. Only when the main
main amplifier will be overloaded with respect to its maximum
output current, it will not longer be able to maintain a ground
potential at its summing junction through the feedback impedance
of the overall amplifier setup. So a deviation from zero at this
point may be savely used as a sign of current overload.

Resistors and capacitors:
A precision analog computer needs precision parts for its
calculation resistors and capacitors. Resistors with a precision
of at least 0.1 percent are required. Really professional analog
computers use 0.01 or even 0.005 percent resistors which are
very (very!) expensive devices. The same holds true for the
capacitors used in integrators and storage cells. These capacitors
should have a precision well below 1 percent and should be
adjustable (by paralleling a trimmer, etc.). Some precision analog
computers have all of these parts mounted in a temperature
controlled oven to ensure constant environmental conditions.

Integrator control:
Every integrator in an analog computer normally uses two relays
to control the run mode of the integrator (initial condition,
run, hold). In cheap (or early) analog computers relays were used
to implement these switches. Relays have some fine properties as
the nearly infinite resistance in the open state and the very low
resistance in the closed state. Apart from these two advantages,
relays have three major drawbacks:

They need a significant amount of time to operate,

even relays from the same batch will have a slightly different
timing and

relays bounce when being switched.

The first problem is not too difficult at all - if fast repetition
times of the computer are desired, the known relay setup times can
simply be taken into account. The third problem can be overcome by
using realys with mercury wetted contacts. The seconds problem is
the main problem - even slightly different times at which the
various integrators in a computer setup will be switched from one
run mode to another will introduce subtle errors into calculations
which are very difficult to analyse and compensate for.

Electronic switches:
A modern precision analog computer would most probably make use of
electronic switches for controlling integrators and storage, etc.
In contrast to relays electronic switches feature negligible
switching delays and they do not bounce at all. Unfortunately there
are two problems with electronic switches, too: In the on-state
they have a resistance far from being zero and in the off-state they
have a finite resistance. Both effects will introduce additional
problems and will require a redesign of integrator and storage
circuits. In some cases it will be better to use three electronic
switches instead of two relays to clamp certain signals, etc.
A good introduction into this area may be found in the
TELEFUNKEN ZEITUNG, Jahrgang 29, 1966, Heft 1 in an article
written by Dr. A. Kley who was a leading figure in the field of
electronic switch design and integrator control.

Additional modes:
Apart from the traditional modes of a simple analog computer
(see above) some more complicated modes will be required in a large
scale precision analog computer:

Potentiometer setup:
This mode will load all coefficient potentiometers as if they
were wired in an active calculation to allow a precise setup of
individual potentiometers. Further more each potentiometer should
be easily selectable for readout on a compensation analog
voltmeter or a precision digital voltmeter (having a resolution
of 4.5 digits at least).

Static check:
This mode will put the computer in a near-run mode but will
switch on special jacks on the patch board which can be used to
introduce synthetic variables into a program. The near-run mode
differs from a real run mode in a way that all integrators
are still in hold mode and their input summing junctions are
grounded (thus the term "static" check - the calculation is
static and time will not influence the state of any device in the
computer).

Balance check:
This mode will place all operational amplifiers into a special
mode featuring a feedback impedance which will result in a very
high amplification (normally about 1000). In addition to this the
inputs of all these amplifiers are grounded so that at their
output only the amplified imbalance of the amplifier can be
measured. Measuring the output voltage of each amplifier they
can be balanced to zero be means of setting their balance
potentiometers.

Repetitive operation:
Many (interesting) calculations require repetitive
operation of the computer in which initial condition setup and
run are performed repetitively. Repetitive operation is useful
for example to display more or less flicker free pictures on an
oscilloscope and allowing the user to change parameters of the
calculation by adjusting potentiometers and see the effects of
those changes immediately.

Iterative operation:
In iterative operation there will be at least two groups of
integrators - a "normal" group and a "complementary" group. While
one group is in run mode, the other group is in hold mode and
vice versa (a bit oversimplified). This mode is ideally suited
for optimization tasks
and other iterative processes to be mapped to the analog
computer.

Multipliers:
Apart from the most simple computational elements as summers and
integrators an analog computer requires devices to perform
multiplication as well. Electronic (precision) multiplication is a
difficult task and some different techniques are normally applied:

Servo multipliers:
At the heart of a servo multiplier are some ten turn
potentiometers mounted on a common shaft which is connected to a
servo motor. An operational amplifier is used to implement a
feedback control circuit which allows to set the rotational angle
of the common shaft depending on some input value (the multiplier).
One of the potentiometers is used to close the feedback loop so
this potentiometer is not available for multiplication. All other
potentiometers located on the common shaft can be fed with
multiplicands which will be automatically multiplied by means of
the rotational shaft angle which is controlled by the multiplier.
Precision servo multipliers have very low errors (down to 0.1
percent)
and they allow the instant multiplication of a variety of
multiplicands with a single multiplier which often comes in handy
in many calculations. Their drawbacks are the very delicate
hardware and their inherent slow speed (limited by the maximum
rotational speed allowed for by the ten turn potentiometers and
the gear box).

Time division multipliers:
These multipliers also allow the multiplication of several
multiplicands with a single multiplier. The idea is to use the
multiplier to control the pulse with of a steady stream of pulses
while the multiplicands are used to control the amplitude of
such a pulse sequence. So multiplier and multiplicand modulate
the X- and Y-dimension of rectangular areas which correspond to
the desired products. These products will be generated by applying
a low pass filter to the pulse outputs of the multiplier. This
kind of multiplier is much faster than a servo multiplier while
still allowing the calculation of several products in parallel.
The pulse width modulation introduces some ripple and noise and
the low pass filter still limits the bandwidth of multipliers like
these.

Parabola multipliers:
Parabola multipliers make use of the fact that
(x + y) ** 2 - (x - y) ** 2 equals 4 * x * y. The only thing
such a multiplier needs are two parabola function generators which
can be quite easily built as diode function generators. The
disadvantages of this technique are that only one product x * y can
be generated at a time and the precision is somewhat lower due
to the use of diode based function generators which approximate
functions by polygons.

Function generators:
Most calculations require the generation of more or less arbitrary
functions. Apart from some quite arcane devices making use of
rare physical effects, most function generators are based on
biased diodes to approximate functions as polygons. Most
professional analog computers featured variable diode function
generators as well as fixed function generators (sine, cosine, log,
exp, etc.).

Curve followers:
Nearly every large analog computer features some special devices
like curve followers and so called photo formers. A curve follower
consists of a XY-plotter with a pickup coil mounted instead of
a pen and a specially prepare sheet of paper on which the desired
function has been drawn with conductive ink or laid out with fine
wire and fixated with some tape on the paper. A high frequency
generator is used to inject a signal into this function wire while
the pickup coil acts as an antenna and is used to form a feedback
loop with the aid of an operational amplifier. So whenever the
X-position of the plotter's carriage changes, the Y-position will
follow the function painted on the paper with conductive ink. The
advantage of such a setup is the ease with which a function can
be generated. Drawbacks are the inherently slow speed and the low
precision.

Photo formers:
A photo former works quite like a curve follower but is based on an
oscilloscope, an opaque mask, a photomultiplier and a feedback
control loop. The desired function is cut out of the opaque mask
which is then placed over the oscilloscope screen in a way that
the beam is blocked by the mask when it is below the function value
at a particular X-position. If it is above the function value at
some X-value it can shine through. This is picked up by a
photomultiplier tube (a modern implementation might use a PIN diode)
which in turn controls a feedback loop. This feedback loop tries
to balance the oscilloscope beam always just at the edge of the
opaque mask. The input to this device is an X-position signal which
directly controls the X-position of the beam while the output is
the Y-position voltage generated by the feedback loop to keep the
dot on the edge of the mask.

Remarks:

As already stated elsewhere: I am an enthusiastic collector of old
computing machinery, especially VAX-systems and analog computers. So I
do NOT collect these items to make any profit! I will NOT sell any
of my machines and I normally can NOT afford to pay for machines
someone wants to give away. All of my money goes into preserving and
maintaining these machines. Questions like "You have so many (analog)
computers, give me one/some of your machines!" are an effrontery!

If you have a system you want to give away to a good home, I would love
to take care of it. If you want to make money from your system, please
do not ask me.

P.S.: I will really not give away any of my machines! Neither to
students writing a thesis nor to anyone else. If I have two machines
of a type I might be willing to swap but do not count on this. This
is a private collection and I love my machines - maybe more than you
can imagine. I will help where ever I can with my knowledge about
these systems and about using, maintaining and programming analog
computers. I will even scan drawings and handbooks to help you in
getting your system running again.

Important:
Today (04-FEB-2007) someone told me that he saved the remains of
a Telefunken RA 741
analog computer from scrap as well as some parts from a RA 770, an
EAI TR-48 and a Systron Donner system - and he told me that he could
not take two EAI-380 systems since he had no room, so these were
scrapped! I am in tears - honestly! It would have taken him a single
phone call (0177 / 5633531) to tell me about the machines - I would
have come with a suitable vehicle and would have taken care of the
two computers!
Please - if you know of a system looking for a good home, let
me know! I will pay for all expenses - I will arrange and/or pay
shipping, I will do everything I can to save analog computers from
scrap! Do not let those systems be scrapped - they are our technological
heritage and they should be preserved! Please help me in preserving
this technology! (And please do not tell me about systems scrapped -
I love machines! It hurts me to hear about such incidents!)